用长除法计算,并写出商式和余式：(x^3-8y^3)/(x-2y).用长除法算的话,每一项都补出来以后怎么做?

Question

用长除法计算,并写出商式和余式：(x^3-8y^3)/(x-2y).用长除法算的话,每一项都补出来以后怎么做?

Answer 1

.x^2+2xy+4y^2
x-2y x^3-8y^3
-.x^3-2x^2y
=.-8y^3+2x^2y
-.-4xy^2+2x^2y
=.4xy^2-8y^3
-.4xy^2-8y^3
=.0
因此：：(x^3-8y^3)/(x-2y) = x^2+2xy+4y^2 .
实际上：（x^3-8y^3）= [x^3-(2y)^3]=(x-2y)(x^2+2xy+4y^2)